It should be noted that besides the area of \({\cal H}^{\pm }\) , the surface gravity of \({\cal H}^{\pm }\) 
is also another important quantity of the thermodynamics. Therefore it may play crucial role to
understanding the entropy at the microscopic level.
Almost all the other thermodynamic properties like first law of thermodynamics, Smarr formula etc.
have discussed in Ref. [1]} so we have not repeated them here.
